Dirac Nodes Research Articles

Self-Assembly of Isostatic Self-Dual Colloidal Crystals.

Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on a nematic monolayer of attractive half-cylindrical colloids to self-assemble these exotic structures. This system can be seen as a 2D system of semidisks. By using MonteCarlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg space-group symmetry and the twisted kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the full phononic spectrum at the self-dual point and the merging of two tilted Weyl nodes into one critically tilted Dirac node. The latter is "accidentally" located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flatbands at the self-dual point, which are linear combinations of "finite-frequency" floppy modes. These modes can be understood as mechanically coupled self-dual rhombus chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties.

Efficient Electrochemical Water Splitting with PdSn4 Dirac Nodal Arc Semimetal

Recently, several researchers have claimed the existence of superior catalytic activity associated with topological materials belonging to the class of Dirac/Weyl semimetals, owing to the high electron conductivity and charge carrier mobility in these topological materials. By means of X-ray photoelectron spectroscopy, electrocatalytic tests, and density functional theory, we have investigated the chemical reactivity (chemisorption of ambient gases), ambient stability, and catalytic properties of PdSn4, a topological semimetal showing Dirac node arcs. We find a Tafel slope of 83 mV in the hydrogen evolution reaction (HER) dec–1 with an overpotential of 50 mV, with performances resembling those of pure Pd, regardless of its limited amount in the alloy, with a subsequent reduction in the cost of raw materials by ∼80%. Remarkably, the PdSn4-based electrode shows superior robustness to CO compared to pure Pd and Pt and high stability in water media, although the PdSn4 surface is prone to oxidation with the formation of a sub-nanometric SnO2 skin. Moreover, we also assessed the significance of the role of topological electronic states in the observed catalytic properties. Actually, the peculiar atomic structure of oxidized PdSn4 enables the migration of hydrogen atoms through the Sn–O layer with a barrier comparable with the energy cost of the Heyrovsky step of HER over Pt(111) in acidic media (0.1 eV). On the other hand, the topological properties play a minor role, if existing, contrarily to the recent reports overestimating their contribution in catalytic properties.

Experimental Observation and Spin Texture of Dirac Node Arcs in Tetradymite Topological Metals.

We report the observation of a nontrivial spin texture in Dirac node arcs, i.e., novel topological objects formed when Dirac cones of massless particles extend along an open one-dimensional line in momentum space. We find that such states are present in all the compounds of the tetradymite M_{2}Te_{2}X family (M=Ti, Zr, or Hf and X=P or As) regardless of the weak or strong character of the topological invariant. The Dirac node arcs in tetradymites are thus the simplest possible textbook example of a type-I Dirac system with a single spin-polarized node arc.

Experimental signatures of the chiral anomaly in Dirac–Weyl semimetals

We provide a review of recent experimental results on the chiral anomaly in Dirac/Weyl semimetals. After a brief introduction, we trace the steps leading to the prediction of materials that feature protected 3D bulk Dirac nodes. The chiral anomaly is presented in terms of charge pumping between the chiral Landau levels of Weyl fermions in parallel electric and magnetic fields. The related chiral magnetic effect and chiral zero sound are described. Current jetting effects, which present major complications in experiments on the longitudinal magnetoresistance, are carefully analyzed. We describe a recent test that is capable of distinguishing these semiclassical artifacts from intrinsic quantum effects. Turning to experiments, we review critically the longitudinal magnetoresistance experiments in the Dirac/Weyl semimetals Na3Bi, GdPtBi, ZrTe5 and TaAs. Alternate approaches to the chiral anomaly, including experiments on non-local transport, thermopower, thermal conductivity and optical pump-probe response are reviewed. In the Supplement, we provide a brief discussion of the chiral anomaly in the broader context of high energy physics and relativistic quantum field theory, as well the anomaly's starring role at the nexus of quantum physics and differential geometry.

A comparative study on the influence of intra- and inter-valley scattering to Hall conductivity of Dirac semimetals

Within the theoretical framework of Kubo linear response theory as well as the self-consistent Born approximation(SCBA), we perform a comparative study about the Hall conductivities of a Dirac semimetal(DSM) subject to, respectively, the intra- and inter-valley scattering. By calculating the Hall conductivity as a function of Fermi level, we find that when the Fermi level lies in the region around the Dirac node, the Hall conductivities between the two cases, i.e. subject to intra- and inter-valley scattering respectively, do not show appreciable difference, regardless of the scattering strength. As the Fermi level goes away from the Dirac node, the Hall conductivity in the case of inter-valley scattering is smaller than that in the case of intra-valley scattering if the scattering has relatively weak or moderate strength. In contrast, as scattering strength increases further, the Hall conductivity spectra between the two cases look almost identical no matter whether the Fermi level is close to or far away from the Dirac node. The underlying physics of these numerical results is that the Fermi surface has nontrivial contribution to the Hall conductivity in the case of weak or moderate scattering. However, in the case of strong scattering, it becomes much smaller than the contribution arising from all the occupied states. In addition, our study indicates that the cone tilt brings about the effective enhancement of Hall conductivity of DSMs.

Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model

We study the effects of static magnetic and electric fields on Kitaev's honeycomb model. Using the electric polarization operator appropriate for Kitaev materials, we derive the effective Hamiltonian for the emergent Majorana fermions to second-order in both the electric and magnetic fields. We find that while individually each perturbation does not qualitatively alter Kitaev spin liquid, the cross-term induces a finite chemical potential at each Dirac node, giving rise to a Majorana-Fermi surface. We argue this gapless phase is stable and exhibits typical metallic phenomenology, such as linear in temperature heat capacity and finite, but non-quantized, thermal Hall response. Finally, we speculate on the potential for realization of this physics in Kitaev materials.

Double Dirac nodal line semimetal with a torus surface state

We propose a class of nodal line semimetals that host an eight-fold degenerate double Dirac nodal line (DDNL) with negligible spin-orbit coupling. We find only 5 of the 230 space groups host the DDNL. The DDNL can be considered as a combination of two Dirac nodal lines, and has a trivial Berry phase. This leads to two possible but completely different surface states, namely, a torus surface state covering the whole surface Brillouin zone and no surface state at all. Based on first-principles calculations, we predict that the hydrogen storage material LiBH is an ideal DDNL semimetal, where the line resides at Fermi level, is relatively flat in energy, and exhibits a large linear energy range. Interestingly, both the two novel surface states of DDNL can be realized in LiBH. Further, we predict that with a magnetic field parallel to DDNL, the Landau levels of DDNL are doubly degenerate due to Kramers-like degeneracy and have a doubly degenerate zero-mode.

Non-Monotonic Evolution of Carrier Density and Mobility under Thermal Cycling Treatments in Dirac Semimetal Cd3As2 MicrobeltsSupported by the National Key Research and Development Program of China (Grant No. 2016YFA0401003), and the National Natural Science Foundation of China (Grant Nos. 11804340, 11774353, U19A2093, and U1732274), and the CAS/SAFEA International Partnership Program for Creative Research Teams of China.

Tunable carrier density plays a key role in the investigation of novel transport properties in three-dimensional topological semimetals. We demonstrate that the carrier density, as well as the mobility, of Dirac semimetal Cd3As2 nanoplates can be effectively tuned via in situ thermal treatment at 350 K for one hour, resulting in non-monotonic evolution by virtue of the thermal cycling treatments. The upward shift of Fermi level relative to the Dirac nodes blurs the surface Fermi-arc states, accompanied by an anomalous phase shift in the oscillations of bulk states, due to a change in the topology of the electrons. Meanwhile, the oscillation peaks of bulk longitudinal magnetoresistivity shift at high fields, due to their coupling to the oscillations of the surface Fermi-arc states. Our work provides a thermal control mechanism for the manipulation of quantum states in Dirac semimetal Cd3As2 at high temperatures, via their carrier density.

Dirac states in the noncentrosymmetric superconductor BiPd

Quantum materials having Dirac fermions in conjunction with superconductivity is believed to be the candidate material to realize exotic physics as well as advanced technology. Angle-resolved photoemission spectroscopy (ARPES), a direct probe of the electronic structure, has been extensively used to study these materials. However, experiments often exhibit conflicting results on dimensionality and momentum of the Dirac fermions (e.g., Dirac states in BiPd, a novel noncentrosymmetric superconductor), which is crucial for the determination of the symmetry, time-reversal invariant momenta, and other emerging properties. Employing high-resolution ARPES at varied conditions, we demonstrated a methodology to identify the location of the Dirac node accurately and discover that the deviation from two dimensionality of the Dirac states in BiPd proposed earlier is not a material property. These results helped to reveal the topology of the anisotropy of the Dirac states accurately. We have constructed a model Hamiltonian considering higher-order spin-orbit terms and demonstrate that this model provides an excellent description of the observed anisotropy. Intriguing features of the Dirac states in a noncentrosymmetric superconductor revealed in this study are expected to have significant implications regarding the properties of topological superconductors.

Anisotropic Berry phase in the Dirac nodal-line semimetal ZrSiS: The effect of spin-orbit coupling

The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the $k$ space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the $c$ axis and magnetic field rotating in the $ab$ plane. The extremal orbits identified through the field orientation dependence of the QOs interlock with the nodal line, leading to a nonzero Berry phase. Most importantly, the Berry phase shows a significant dependence on the magnetic field orientation, which we argue to be due to the finite spin-orbit coupling gap. Our results demonstrate the importance of the spin-orbit coupling and the nodal-line dispersion in understanding the quantum transport of NLSMs.

Spectroscopic evidence for the realization of a genuine topological nodal-line semimetal in LaSbTe

Numerous nodal-line semimetal candidates have been predicted and experimentally examined. To realize a genuine nodal-line semimetal, the Dirac nodes must be robust against spin-orbit coupling and must lie close to the Fermi level so as to allow for the manifestation of the novel properties. By performing band structure calculations and angle-resolved photoemission measurements, direct evidence is provided here for the realization of a genuine nodal-line semimetal in LaSbTe. This finding creates new opportunity for exploring novel phenomena in topological materials.

Strain engineering the topological type-II Dirac semimetal NiTe2

In the present work, we investigated the electronic and elastic properties in equilibrium and under strain of the type-II Dirac semimetal NiTe$_2$ using density functional theory (DFT). Our results demonstrate the tunability of Dirac nodes' energy and momentum with strain and that it is possible to bring them closer to the Fermi level, while other metallic bands are supressed. We also derive a minimal 4-band effective model for the Dirac cones which accounts for the aforementioned strain effects by means of lattice regularization, providing an inexpensive way for further theoretical investigations and easy comparison with experiments. On an equal footing, we propose the static control of the electronic structure by intercalating alkali species into the van der Waals gap, resulting in the same effects obtained by strain-engineering and removing the requirement of in situ strain. Finally, evaluating the wavefunction's symmetry evolution as the lattice is deformed, we discuss possible consequences, such as Liftshitz transitions and the coexistence of type-I and type-II Dirac cones, thus motivating future investigations.

Prediction of two-dimensional Cu2C with polyacetylene-like motifs and Dirac nodal line

The design of novel two-dimensional (2D) materials with unique atomistic configurations and exotic properties are highly desirable for material science. Here, we report the prediction of 2D ${\mathrm{Cu}}_{2}\mathrm{C}$ layers featuring unique carbon motifs with Dirac nodal lines through evolutionary algorithm searches in conjunction with first-principles calculations. The global minimum $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Cu}}_{2}\mathrm{C}$ is an exciting new structure featuring one-dimensional (1D) zigzag carbon chains sandwiched by two hexagonal-close-packed copper monolayers, conferring to our predicted ground-state 2D $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Cu}}_{2}\mathrm{C}$ an inverse coordination structure. This polyacetylene-like motif $(\mathrm{poly}\text{\ensuremath{-}}{\mathrm{C}}_{2})$ is also encountered in $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Cu}}_{2}\mathrm{C}$. Remarkably, the electronic band structure of $\ensuremath{\alpha}$ and $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Cu}}_{2}\mathrm{C}$ phases containing polyacetylene-like chains display a 1D Dirac nodal line, which is protected by the glide plane symmetry. Fermi velocities $({v}_{f})$ as high as $2.45\ifmmode\times\else\texttimes\fi{}{10}^{5}$ and $3.85\ifmmode\times\else\texttimes\fi{}{10}^{5}$ m/s are calculated for $\ensuremath{\alpha}$ and $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Cu}}_{2}\mathrm{C}$ phases, respectively. This work is an effective effort to design and stabilize the 2D copper carbide layers with exotic structures and nodal lines.

Thermal transport in superconductors with coexisting spin density wave order

We study thermal transport in a two-dimensional system with coexisting $s$- or $d$-wave Superconducting (SC) and Spin Density Wave (SDW) orders. We analyse the nature of coexistence phase in a tight-binding square lattice with $\mathbf{Q}=(\pi,\pi)$ SDW ordering. The electronic thermal conductivity is computed within the framework of the Boltzmann kinetic theory, using Born approximation for the impurity scattering collision integral. We describe the influence of the Fermi surface (FS) topology, the competition between the SC and SDW order parameters, the presence or absence of zero energy excitations in the coexistence phase, on the low temperature behavior of thermal conductivity of the various paring states. We present qualitative analytical, and fully numerical results that show that the heat transport signatures of various SC states emerging from collinear SDW order are quite distinct, and depend on the symmetry properties of the SC order parameter under translation by the SDW nesting vector $\mathbf{Q}$. {A combination of $(\pi,\pi)$-SDW and the $d_{x^2-y^2}$ pairing state results in fully gapped excitations, whereas $(\pi,\pi)$-SDW co-existing with either $d_{xy}$ or $s$-wave pairing states may always have gapless excitations. There appear special stable Dirac nodal points that are not gapped by the SC order in the coexistence phase, resulting in finite residual heat conductivity.

Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids

Spin-orbital liquids are quantum disordered states in systems with entangled spin and orbital degrees of freedom. We study exactly solvable spin-orbital models in two dimensions with selected Heisenberg-, Kitaev-, and $\mathrm{\ensuremath{\Gamma}}$-type interactions, as well as external magnetic fields. These models realize a variety of spin-orbital-liquid phases featuring dispersing Majorana fermions with Fermi surfaces, nodal Dirac or quadratic band touching points, or full gaps. In particular, we show that Zeeman magnetic fields can stabilize nontrivial flux patterns and induce metamagnetic transitions between states with different topological character. Solvable nearest-neighbor biquadratic spin-orbital perturbations can be tuned to stabilize zero-energy flat bands. We discuss in detail the examples of $\mathrm{SO}(2)$- and $\mathrm{SO}(3)$-symmetric spin-orbital models on the square and honeycomb lattices, and use group-theoretical arguments to generalize to $\mathrm{SO}(\ensuremath{\nu})$-symmetric models with arbitrary integer $\ensuremath{\nu}>1$. These results extend the list of exactly solvable models with spin-orbital-liquid ground states and highlight the intriguing general features of such exotic phases. Our models are thus excellent starting points for more realistic modelling of candidate materials.

Colossal Terahertz Photoresponse at Room Temperature: A Signature of Type-II Dirac Fermiology.

The discovery of Dirac semimetal has stimulated bourgeoning interests for exploring exotic quantum-transport phenomena, holding great promise for manipulating the performance of photoelectric devices that are related to nontrivial band topology. Nevertheless, it still remains elusive on both the device implementation and immediate results, with some enhanced or technically applicable electronic properties signified by the Dirac fermiology. By means of Pt doping, a type-II Dirac semimetal Ir1-xPtxTe2 with protected crystal structure and tunable Fermi level has been achieved in this work. It has been envisioned that the metal-semimetal-metal device exhibits an order of magnitude performance improvement at terahertz frequency when the Fermi level is aligned with the Dirac node (i.e., x ∼ 0.3) and a room-temperature photoresponsivity of 0.52 A·W-1 at 0.12 THz and 0.45 A·W-1 at 0.3 THz, which benefited from the excitation of type-II Dirac fermions. Furthermore, van der Waals integration with Dirac semimetals exhibits superb performance with noise equivalent power less than 24 pW·Hz-0.5, rivaling the state-of-the-art detectors. Our work provides a route to explore the nontrivial topology of Dirac semimetal for addressing targeted applications in imaging and biomedical sensing across a terahertz gap.

Evidence for a large Rashba splitting in PtPb4 from angle-resolved photoemission spectroscopy

We studied the electronic structure of PtPb$_{4}$ using laser angle-resolved photoemission spectroscopy(ARPES) and density functional theory(DFT) calculations. This material is closely related to PtSn$_{4}$, which exhibits exotic topological properties such as Dirac node arcs. Fermi surface(FS) of PtPb$_{4}$ consists of two electron pockets at the center of the Brillouin zone(BZ) and several hole pockets around the zone boundaries. Our ARPES data reveals significant Rashba splitting at the $\Gamma$ point in agreement with DFT calculations. The presence of Rashba splitting may render this material of potential interest for spintronic applications.

Ultrafast investigation and control of Dirac and Weyl semimetals

Ultrafast experiments using sub-picosecond pulses of light are poised to play an important role in the study and use of topological materials and, particularly, of the three-dimensional Dirac and Weyl semimetals. Many of these materials’ characteristic properties—their linear band dispersion, Berry curvature, near-vanishing density of states at the Fermi energy, and sensitivity to crystalline and time-reversal symmetries—are closely related to their sub- and few-picosecond response to light. Ultrafast measurements offer the opportunity to explore excitonic instabilities and transient photocurrents, the latter depending on the Berry curvature and possibly quantized by fundamental constants. Optical pulses may, through Floquet effects, controllably and reversibly move, split, merge, or gap the materials’ Dirac and Weyl nodes; coherent phonons launched by an ultrafast pulse offer alternate mechanisms for similar control of the nodal structure. This Perspective will briefly summarize the state of research on the ultrafast properties of Dirac and Weyl semimetals, emphasizing important open questions. It will describe the challenges confronting each of these experimental opportunities and suggest what research is needed for ultrafast pulses to achieve their potential of controlling and illuminating the physics of Dirac and Weyl semimetals.

Dirac polaron dynamics in the correlated semimetal of perovskite CaIrO3

We have investigated the charge dynamics of the correlated Dirac semimetallic perovskite ${\mathrm{CaIrO}}_{3}$ by infrared spectroscopy. The optical conductivity spectra show the $\ensuremath{\omega}$-linear-type interband transition and a tiny Drude response at low temperatures, suggesting that the Dirac node is pinned near the Fermi energy due to the Mott criticality. Moreover, a large polaron absorption appears at around 0.04 eV, when thermally excited carriers diminish and the plasma frequency decreases below the optical phonon energy. The electron correlation and resultant reduced plasma frequency are likely to enhance the electron-phonon interaction via the insufficient electronic screening, realizing the Dirac polaron.

Dirac Loops in a Strongly Correlated Metal: Origin of Large Magnetoresistance?

Researchers have discovered an extremely large magnetoresistance effect in a high-quality single crystal of β-ReO2, where high-mobility minority carriers relevant to the Dirac nodal loops coexist with majority carriers with a strong electron correlation.